Handbook of dynamics and probability / Peter Müller.
Müller, Peter K.
2022
QA805
Available Online

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Title Handbook of dynamics and probability / Peter Müller.
Author Müller, Peter K.
ISBN 9783030884864 (electronic bk.)
3030884864 (electronic bk.)
3030884856
9783030884857
DOI https://doi.org/10.1007/978-3-030-88486-4
Imprint Cham, Switzerland : Springer, [2022]
Language English
Description 1 online resource
Other Standard Identifiers 10.1007/978-3-030-88486-4 doi
Call Number QA805
Dewey Decimal Classification 515/.39
Summary Our time is characterized by an explosive growth in the use of ever more complicated and sophisticated (computer) models. These models rely on dynamical systems theory for the interpretation of their results and on probability theory for the quantification of their uncertainties. A conscientious and intelligent use of these models requires that both these theories are properly understood. This book is to provide such understanding. It gives a unifying treatment of dynamical systems theory and probability theory. It covers the basic concepts and statements of these theories, their interrelations, and their applications to scientific reasoning and physics. The book stresses the underlying concepts and mathematical structures but is written in a simple and illuminating manner without sacrificing too much mathematical rigor. The book is aimed at students, post-docs, and researchers in the applied sciences who aspire to better understand the conceptual and mathematical underpinnings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many technical aspects covered in appendices, but does require some basic knowledge in analysis, linear algebra, and physics. Peter Müller, now a professor emeritus at the University of Hawaii, has worked extensively on ocean and climate models and the foundations of complex system theories.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed December 6, 2021).
Available in Other Form Print version: 9783030884857
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Introduction
I Dynamics
Deterministic dynamical systems
Linear and integrable systems
Stability and long-time behavior
Ergodic theory
Numerical Algorithms
II Probability
Probability Theory
Discrete-time stochastic processes
Continuous-time stochastic processes
Information entropy
III Probability in dynamical evolution
Time evolution of broadened initial states
Stochastic processes generated by observables
Stochastic dynamical systems
IV Probability in scientific reasoning
Interpretations of probability
Parameter estimation and hypothesis testing
Bayesian inferences
V Probability in physics
Equilibrium statistical mechanics
Non-equilibrium statistical mechanics
Foundational issues of statistical mechanics
Quantum Mechanics
A Classical Mechanics
B Thermostatics
C Fluid dynamics
D Some proofs and explicit computations
E Mathematical tools, conventions and notation
References
Index.

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